Question

serious help here... trying to construct a polynomail with *Real coefficients*Two imaginary zeros*One real zero that is POS and touches x axis*one real zero that is NEG fraction that corsses x axis.. PLEASE help me somebody have been on this problem wayy too long??

Answer 1

i have -(x+1)(x^2+1)(x^2-1)(2x+5)^2... am i close.. ?

Answer 2

that looks good to me, let me graph it just to check.

Answer 3

it touches at the x axis, but it doesn't have a neg fraction crossing at x.. ?? or does it and i cnt see it well on this tiny graph

Answer 4

The (2x+5) takes care of the negative fraction. what you have is good. In fact you could take some stuff off and it would still be right.

Answer 5

oh, but you need the negative fraction root to cross the x axis, so take off the square from the (2x+5)

Answer 6

oh my

Answer 7

perfect

Answer 8

im not sure if that is just the vertical asymptote that i see, but i think it does cross it.. and touches at the neg x axis which is the 2x+5...

Answer 9

so what would my real zeros be?

Answer 10

-5/2

Answer 11

im getting confused with all the requirements lol >.< one by one:
Two Imaginary roots: (x^2+1)
One positive Real root that just touches the x axis: (x-1)^2
One negative fractional root that crosses the x axis: (2x+5)

All together now:

(x^2+1)(x-1)^2(2x+5)

Answer 12

that one just touches x axis?

Answer 13

requirements
1. real coef
2. two imaginary zeros
3. one real zero that is pos and touches the x axis
4one real zero that is neg fraction and crosses the x axis
5. end behavior

Answer 14

wonder if she couls have added just one more requirement LOL.. sheesh...

Answer 15

i think original -(x+1)(x^2+1)(x^2-1)((2x+5) works, you wre right, i just had to get rid of that square from the end

Answer 16

is it a single poly, or is it a separate poly for each requirement?

Answer 17

all for one polynomial function, with those characteristics...
:)

Answer 18

Ihave calculated it over and over, seems like it will work, the -(x^2+1)(x-1)^2(2x+5)

Answer 19

it look ok?

Answer 20

it wants to know the maximum number of turning points and why, and also would like to know the minimum number of turning points?

Answer 21

my first min is -1.849973=x and y=-46.69828... do i use the x value or y? ive been told x, but a math professor said y.. got me confused

Answer 22

*Real coefficients - this happens regardless

*Two imaginary zeros - it has a bend above or below the axis



*One real zero that is POS and touches x axis - touch and go



*one real zero that is NEG fraction that corsses x axis - has an (ax+b) format